Quadratic systems with an invariant conic having Darboux invariants

The complete characterization of the phase portraits of real planar quadratic vector fields is very far to be completed. As this attempt is not possible in the whole class due to the large number of parameters (twelve, but, after affine transformations and time rescaling, we arrive at families with...

Descripción completa

Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Oliveira, Regilene|||0000-0002-9628-5180
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:199334
Acceso en línea:https://ddd.uab.cat/record/199334
https://dx.doi.org/urn:doi:10.1142/S021919971750033X
Access Level:acceso abierto
Palabra clave:Darboux invariant
Phase portraits
Quadratic vector fields
Descripción
Sumario:The complete characterization of the phase portraits of real planar quadratic vector fields is very far to be completed. As this attempt is not possible in the whole class due to the large number of parameters (twelve, but, after affine transformations and time rescaling, we arrive at families with five parameters, which is still a big number of parameters), many subclasses have been considered and studied. In this paper we complete the characterization of the global phase portraits in the Poincaré disc of all planar quadratic polynomial differential systems having an invariant conic and a Darboux invariant, constructed using only the invariant conic.